The present invention relates to a capacitive dynamic quantity sensor, a method for manufacturing the capacitive dynamic quantity sensor, and a detector including the capacitive dynamic quantity sensor.
For example, a capacitive semiconductor acceleration sensor shown in FIG. 7A is such a capacitive dynamic quantity sensor. As shown in FIGS. 7A and 7B, in the acceleration sensor, a weight 11 is supported by anchors 13, which are fixed to a semiconductor substrate 1, through springs 12. First and second comb-tooth-like movable electrodes 10a, 10b are integrated with the weight 11. As illustrated in FIG. 7A, first and second comb-tooth-like fixed electrodes 15a, 15b, which respectively face the first and second movable electrodes 10a, 10b, are supported at one ends thereof by first and second electrode wiring lines 16a, 16b. 
When acceleration is detected, predetermined voltages are applied between movable electrode pad 14 for the movable electrodes 10a, 10b and fixed electrode pads 17a, 17b for the fixed electrodes 15a, 15b. With the voltages, first and second capacitances CS1 and C2 are formed respectively between the first movable electrodes 10a and the first fixed electrodes 15a and between the second movable electrodes 10b and the second fixed electrodes 15b. CS1 and CS2 are expressed by the following equation eq. 1 when no acceleration is applied,CS1=CS2=∈×n×L×h1×(1/d1+1/d2)  eq. 1where ∈ is dielectric constant, n is the number of each group of the movable electrodes, L is the effective electrode length, which is the length of the surfaces at which the movable and fixed electrodes face, h1 is the electrode height, which is the height of the surfaces at which the movable and fixed electrodes face, and d1 and d2 are respectively the dimension of the narrow gaps between the electrodes and the dimension of the wide gaps between the electrodes. In the acceleration sensor shown in FIG. 7A, each of the electrodes has the same effective electrode length L and the same electrode height h1.
When the sensor is accelerated, the springs 12 deform to vary the dimensions d1 and d2, or the distances d1 and d2 between the movable electrodes 10a, 10b and the fixed electrodes 15a, 15b. However, the dimension d2 of the wide gaps is sufficiently greater than the dimension d1 of the narrow gaps, so the first and second capacitances CS1 and CS2 vary with the distance variation. Therefore, the acceleration can be measured by detecting the capacitance difference ΔC, or (CS1−CS2), between the first and second capacitances CS1 and CS2.
Specifically, for example, if the sensor is accelerated to displace the first movable electrodes 10a by Δd in the direction shown by arrows in FIGS. 7A and 7C, the dimension d1 of the narrow gaps narrow by Δd and the wide gaps d2 widen by Δd between the first movable electrodes 10a and the first fixed electrodes 15a to increase the first capacitance CS1, as shown in FIG. 7C. On the other hand, on the cross-section taken along the line VIIC—VIIC in FIG. 7A, the dimension d1 of the narrow gaps widens by Δd and the dimension d2 of the wide gaps narrows by Δd between the second movable electrodes 10b and the second fixed electrodes 15b to decrease the second capacitance CS2. As a result, the capacitance difference ΔC increases.
More specifically, when the sensor is accelerated to displace the first movable electrodes 10a by Δd in the direction shown by arrows in FIGS. 7A and 7C, the narrow gaps become (d1−Δd) and the wide gaps become (d2+Δd) between the first movable electrodes 10a and the first fixed electrodes 15a. On the other hand, the narrow gaps become (d1+Δd) and the wide gaps become (d2−Δd) between the second movable electrodes 10b and the second fixed electrodes 15b. Therefore, from eq. 1, ΔC, or (CS1−CS2), can be expressed by the following equation.ΔC=∈×n×L×h1×[{1/(d1−Δd)+1/(d2+Δd)}−{1/(d1+Δd)+1/(d2−Δd)}]=∈×n×L×h1×2Δd×{1/(d12−Δd2)−1/(d22−Δd2)}
Here, Δd is sufficiently small in comparison with d1 and d2. Therefore, ΔC can be expressed by the following equation eq. 2.ΔC≈∈×n×L×h1×2Δd×(1/d12−1/d22)  eq. 2
The sensor sensitivity can be improved by increasing the variation in capacitance per unit acceleration, that is, ΔC in eq. 2. As understood from eq. 2, ΔC can be increased by sufficiently increasing d2 in comparison with d1.
However, it is difficult to sufficiently improve the sensor sensitivity by adjusting the distances between the electrodes because the dimension d2 of the wide gaps is limited by the dimensions of the sensor.